Evento
Descrizione:
Abstract: A very classical result, the Castelnuovo Lemma, states that, given d+3 points in general position in P^d, there is a unique rational normal curve of degree d passing through them. An easy argument shows that asking for a rational normal curve to pass through a point, imposes, in the parameter spaces of rational normal curves, the same number of conditions imposed by asking for a rational normal curve to be (d-1)-secant to a codimension 2 projective subspace of P^d. For this reason, it is quite natural to pose the following problem: given p points in P^d and l codimension 2 subspaces in P^d with p+l=d+3, is there a rational normal curve passing through the points and being (d-1)-secant to the l projective subspaces? A paper of Carlini and Catalisano (2007) solves all the cases except for (p,l)=(0,d+3). In this talk we show how to solve this missing case by using symmetric polynomials.